An Introduction to Wavelet Analysis [Paperback]

This book provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and analysis of wavelet bases. It motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, then shows how a more abstract approach allows readers to generalize and improve upon the Haar series. It then presents a number of variations and extensions of Haar construction.

D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material . . . than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform . . . The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended!

Bulletin of the AMS

An Introduction to Wavelet Analysis provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases.

The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book elucidates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows one to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical prerequisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts.&llñ